Computably Uncountable
We are all familiar with Cantor’s diagonal argument that proves there exist infinite sets which are “larger” than the set of natural numbers. In this post I will show that we can express this argument in the form of a program, thus showing that there are countable sets which are “computably uncountable”. I begin with [...]
What was the probability of that?
A group of college students bask in their crude weekly haven of Texas Hold’em poker. Amid the usual banter, they watch as one deals out the flop: a three of spades, a three of diamonds, and a three of clubs. The room falls silent and tensions are suspended as if the ground had fallen out [...]
Sentences and Paradigms
As our understanding progresses, what once were rigid distinctions tend to become blurred. Hence, I am fascinated by the pervasiveness and stability of the three programming language paradigms: imperative, functional (here I mean that word in the pure sense, not HOFs sense — Conal Elliott would probably have me call it denotational), and logical. Whole [...]
Relativism and Language
It is hard for me to imagine that so many people are so wrong. Sure, core beliefs go unexamined. Yes, we often unconsciously repeat taglines we have heard from those we respect instead of attempting to translate our true views. But I must admit I think of all people as essentially wanting to figure it [...]
Perspectives on Truth and Realism
Lately I have been considering myself a relativist. To cast away the kneejerks, I don’t consider all belief systems equally valid (with caveats1). Wikipedia sums it up nicely: … that truth is always relative to some particular frame of reference, such as a language or a culture. I have noticed an increase in my opposition [...]
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